Abstract

Employing the language of Lie Groups and Lie Algebras to describe conformal transformations, we identify in a conformal invariant theory Noether charges as the generators of these transformations. We establish the Goldstone theorem and the rules for counting the number of indepedent Goldstone modes in general for systems with and without Lorentz invariance, and discuss various theorems regarding the counting of these Goldstone modes. We conclude with a discussion on conformal invariance, relating the dilatation and special conformal transformation in systems for which translational invariance is not entirely broken.